Fans are divided over this controversial 'Game of Thrones' theory about Tyrion

HBO Warning: There are major spoilers ahead for "Game of Thrones," including speculation of future events.

Tyrion Lannister is one of the main characters — if not the main character— in George R. R. Martin's "A Song of Ice and Fire" series.

And in the second episode of season six, Tyrion had a major story arch in Meereen involving Daenerys Targaryen's two dragons Viserion and Rhaegal that she chained up in season four.

The scene will likely reignite one controversial fan theory that could influence the way you watch this season, and it all has to do with Tyrion's parentage. While it's officially believed that Tywin Lannister and his cousin Joanna were Tyrion's biological parents, there is another controversial theory that suggests Tyrion's real father was the mad king Aerys Targaryen.

If it's true, that would make Tyrion Daenerys' half-brother and (possibly) Jon Snow's uncle.

But fans are divided, either loathing or loving this "secret Targaryen" theory. Let's break down the evidence both for and against "A + J = T" below.

Arguments for Tyrion as a secret Targaryen

The Mad King Aerys lusted after Tyrion's mother Joanna

HBO Barristan Selmy tells Daenerys in "A Dance with Dragons" that her father Aerys wanted to sleep with Joanna Lannister on her wedding night to Tywin:

Prince Aerys...as a youth, he was taken with a certain lady of Casterly Rock, a cousin of Tywin Lannister. When she and Tywin wed, your father drank too much wine at the wedding feast and was heard to say that it was a great pity that the lord's right to the first night had been abolished. A drunken jape, no more, but Tywin Lannister was not a man to forget such words, or the...the liberties your father took during the bedding.

Though there's no word what those bedding liberties were, it's pretty clear that Aerys lusted after Joanna. There was even a rumor in Westeros that Joanna had been Aerys' mistress when she was younger, perhaps even losing her maidenhead to him, before she was dismissed as a lady-in-waiting by the future queen Princess Rhaella Targaryen.

Grand Maester Pycell, however, argues those claims are "baseless" since Tywin was a "proud man and not one accustomed to feasting on another man's leavings."

Still, the seeds were planted that Aerys was more fond of Joanna than was acceptable.

The "A + J = T" timing makes a lot of sense

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One of the biggest critiques of this theory is that the timing of Joanna with Aerys doesn't match with Tyrion's conception. After Joanna was dismissed by Queen Rhaella, she was said to have rarely visited King's Landing afterwards and lived her days at Casterly Rock.

But George R. R. Martin's recent book "A World of Ice and Fire" makes a distinct point of mentioning that Joanna attended the anniversary tourney in King's Landing in 272 AC, which was held to celebrate King Aerys' tenth year on the throne. During this tournament, we also learned King Aerys insulted Joanna by asking her if nursing her children had ruined her breasts.

The next day Tywin, who was also present at the tourney, tried to resign as Hand of the King, but King Aerys refused him. Perhaps Tywin tried to resign because of Aerys' insult to his wife, or perhaps it was because something much more serious had occurred.

Less than a year later, Joanna died giving birth to Tyrion in 273 AC.

Tyrion's mother died during childbirth, just like Jon Snow's and Daenerys' mothers

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Both Tywin and Cersei constantly remind Tyrion that he's the reason Joanna died while giving birth to him. They call him names like "murderer" and "monster," but coincidentally (or not so coincidentally) he may share this trait with two other main characters in the series: Daenerys and Jon Snow.

Daenerys Targaryen was born during a storm on Dragonstone and her mother Rhaella died following complications from her birth. Jon Snow, if a major fan theory is to be believed, is also a Targaryen and his mother Lyanna Stark died during childbirth at the Tower of Joy.

Though it's not necessary for a mother to die to give birth to a Targaryen, this coincidence cements the three main characters together, and could be a major clue that they may be tied to one another.

Tywin rejects Tyrion repeatedly

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Tywin is said to hate Tyrion because he killed Joanna during childbirth as well as because Tyrion makes a mockery of House Lannister with his physical appearance, drinking, and whoring.

"Men's laws give you the right to bear my name and display my colors, since I cannot prove that you are not mine," Tywin tells Tyrion harshly in "A Storm of Swords."

This is a horrible thing to say to your son, but it also besmirches Joanna's name in the process since it assumes she had an affair or was intimate with a man who wasn't Tywin.

Tywin loved Joanna; it was said he may have been the Hand of the King but he "was ruled at home by his lady wife." So why would he question her honor in order to merely insult his son?

Furthermore, Tywin rejects Tyrion as his heir. Because Jaime became a Knight of the Kingsguard, he was never allowed to marry, own land, or father children for the rest of his life. Tyrion should have become Tywin's next rightful heir to the Lannister lands, but Tywin outright refused him.

If "A + J = T" is true, it could be an explanation for why Tywin refused to give Tyrion Lannister property. Aerys not only took away Tywin's only heir by making Jaime a Knight of the Kingsguard, but made it so his bastard son was the only other heir to Casterly Rock.

Tywin would have hated that.

And finally, we're left with Tywin's final words to Tyrion right before Tyrion murders him: "You are no son of mine." Could he have actually been telling the truth?

Tyrion looks more like a Targaryen than a Lannister

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Jon Snow describes Tyrion in "A Game of Thrones" as having a mixture of hair "so blonde it seemed white" and black hair. His white-blonde hair sounds a lot more like the silvery hair of the Targaryens than the golden yellow locks of his Lannister siblings.

Tyrion also has one green eye and one black eye. While having green eyes is a Lannister trait, there is a character named Shiera Seastar in "A Song of Ice and Fire" history who was the bastard of a Targaryen king and had two different colored eyes, just like Tyrion. It could suggest the duality of his parentage, too.

Since we know "the seed is strong" and appearance is a major clue for parentage in Martin's series, Tyrion's image should not be overlooked.

Tyrion may have had 'Dragon Dreams'

HBO There are many Targaryens, including Daenerys, who have seemingly prophetic dreams about dragons.

Tyrion, as it turns out, also has dreamt about dragons. He was obsessed with them as a child and admits he had a "morbid fascination with dragons."

When he was still a lonely child in the depths of Casterly Rock, he oft rode dragons through the nights, pretending he was some lost Targaryen princeling, or a Valyrian dragonlord soaring high o'er fields and mountains. Once, when his uncles asked him what gift he wanted for his nameday, he begged them for a dragon. "It wouldn't need to be a big one. It could be little, like I am." His uncle Gerion thought that was the funniest thing he had ever heard, but his uncle Tygett said, "The last dragon died a century ago, lad." That had seemed so monstrously unfair that the boy had cried himself to sleep that night.

Tyrion knows so much about dragons, in fact, that in "A Dance with Dragons" he's even asked to write a history of dragons by a boy named Griff (more on him later). All of this points to the fact that Tyrion may have a unique relationship with dragons.

Some readers even wonder if he could one day ride one. But just because you dream about dragons, doesn't mean those dreams will come true.

Arguments against Tyrion as a secret Targaryen

Tyrion is too much like Tywin

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Critics of the "Tyrion = Targaryen" theory argue that Tyrion is too much like Tywin not to be his son.

Numerous other characters notice this as well. While speaking with Jaime, Tywin's sister Genna points out how alike Tyrion and Tywin are to one another:

Jaime, sweetling, I have known you since you were a babe at Joanna's breast. You smile like Gerion and fight like Tyg and there's some of Kevan in you, else you would not wear that cloak... but Tyrion is Tywin's son, not you. I said so once to your father's face, and he would not speak to me for half a year.

Tyrion is loyal to his family, wants to further the Lannister name (at least at the beginning of the series), is bold, intelligent, and diplomatic. He's also ruthless, calculated, and enterprising, just like Tywin.

But because he was born a dwarf and not as dashing as his older siblings, Tyrion is rejected by his father.

It also may be that Tywin sees too much of himself in Tyrion. When Tyrion kills his father, it's because he finds him in bed with Shae, a prostitute — something that the upright Tywin was said to have abhorred. Perhaps Tywin really hates Tyrion because he is too much like himself.

Still, it's worth mentioning that there is another bastard in this series who was very much like his supposed father: Jon Snow. Not only does he look more like a Stark than his siblings, but Melisandre said of him that "the only gods he worshipped were honor and duty," not unlike the man who raised him, Ned Stark.

But if certain fan theories are to be believed, Jon Snow is not Ned Stark's son at all. Could Tyrion's personality simply be a case of nature versus nurture, not unlike Jon's?

There are too many secret Targaryens

HBO

If Tyrion was the only secret Targaryen in the series, maybe more fans could come around to the theory. But for many, there are just too many secret Targaryen plots to be believed.

First, there's Jon Snow. If the "R + L = J" theory holds true, that means Jon is the son of Prince Rhaegar Targaryen and Lyanna Stark, making him the nephew of Daenerys and an heir to the Iron Throne in his own right.

And in "A Dance with Dragons," there's also the boy named Griff who Tyrion believes could be Aegon Targaryen, the son of Rhaegar Targaryen (Daenerys' brother and Jon Snow's potential father) and Elia Martell. While many people in Westeros believe Aegon was murdered as a baby on the orders of Tywin Lannister, it's suggested that Aegon may have been spirited away from King's Landing in the nick of time and raised to be king in secret.

Whether or not Griff is a Targaryen is also hotly debated by fans, but it does seem like there are too many secret Targaryen theories out there for all of them to be true.

It's simply not George R. R. Martin's style

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The main argument by those who believe there's no way Tyrion is a Targaryen is that it would be a better story if he wasn't.

George R. R. Martin is an acclaimed writer who developed a complicated, cynical world for his characters where no one is safe and happy endings don't exist. While some fan theories (ahem, "R + L = J") are more neat, the majority of Martin's writing is twisted, complex, and an unforgiving look at the heart of humanity.

Take Tyrion. If he is a secret Targaryen and the product of adultery and/or rape, it would give Tywin an excuse to hate Tyrion. Suddenly, the years of abuse and neglect Tyrion suffered would have an explanation instead of just outright hatred, prejudice, self-loathing, and rejection.

If the "Tyrion = Targaryen" theory is true, the frustrating, Shakespearean melodrama surrounding Tyrion and his father would be for naught.

It just seems a bit too simple for an author like Martin.

So what does this all mean for season six?

Watching Tyrion evolve this season is going to be fascinating since we are now past the point where Martin has written about him in "A Song of Ice and Fire."

Tyrion is currently trying to help rule in Meereen while Daenerys is gone and has now met with her two dragons Viserion and Rhaegal that she chained up at the end of season four.

Tyrion was able to walk into the chamber where they were chained up and stay alive, which is something that should not be taken for granted given how they reacted to Daenerys back in season five. Previously when she tried to visit them in the first episode of last season, they were wild, angry, and breathed fire at her. In the books, one character even died while trying to free them.

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Yet Tyrion lived.

His knowledge and connection with the dragons will likely be instrumental this season — whether or not that's linked to his Targaryen parentage remains to be seen.